Kavita Bhansali-05-Hedging performance

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M P Birla Institute of Management 2

DECLARATION

I hereby declare that the dissertation entitled “Hedging

performance and basis risk in stock index futures” is the result of

work undertaken by me, under the guidance of Dr.T.V.N.Rao,

Associate Professor, M.P.Birla Institute of Management,

Bangalore.

I also declare that this dissertation has not been submitted to any

other University/Institution for the award of any Degree or

Diploma.

Place: Bangalore

Date : 13th

May 2007




ACKNOWLEDGEMENT

It’s my special privilege to extend words of the thanks to all of

them who have helped me and encouraged me in completing the

project successfully.

I would thank Dr.T.V.N.Rao for giving me valuable inputs

required for completing this project report successfully. I owe my

sincere gratitude to him for spending his valuable time with me

and for his guidance.

It would be improper if I do not acknowledge the help and

encouragement by my friends and well wishers who always helped

me directly or indirectly.

My gratitude will not be complete without thanking the almighty

god and my loving parents who have been supportive through out

the project.

Kavita Bhansali




TABLE OF CONTENTS

CHAPTERS PARTICULARS

PAGE NO.

ABSTRACT 02

1 INTRODUCTION AND THEORETICAL

BACKGROUND

03

2 REVIEW OF LITERATURE 46

3 RESEARCH METHODOLOGY 49

4 PROBLEM STATEMENT 50

5 OBJECTIVE OF THE STUDY 50

6 SAMPLE SIZE AND DATA SOURCES 51

7 TEST OF STATIONARITY 5

9 LIMITATIONS OF THE RESEARCH 55

10 DATA ANALYSIS 56

11 CONCLUSION 66

12 ANNEXTURE 67

13 BIBLIOGRAPHY 68




ABSTRACT

Corporation in which individual investor place their money have exposure to

fluctuation of all kinds of financial price, as a natural by product of their operation.

Financial prices include foreign exchange rate, interest rates, commodity prices

and equity prices. The effect of changes in prices reported on earnings is

overwhelming.

Hedging is a way of reducing some of the risk involved in holding an investment.

There are many financial instruments which are used in hedging. In considering

potential application of index futures, it is clear that in nearly every case a cross

hedge is involved. That is the stock position that is being hedge is different from

the underlying portfolio of index contract. This means that the return and risk for

an index futures hedge will depend upon the behavior of “Basis” i.e., the

difference between the futures prices and cash prices. Hedging a position in

stock will necessarily expose it to some measure of Basis risk – risk that the

change in future price over time will not track exactly the value of cash position.

This paper will examine the basis and different sources of basis risk in NSE’s

NIFTY index contract. It will also simplify the theory of hedging in a presence of

basis risk and displays the risk return combination that could have been achieved

in practice by hedging some broadly diversified portfolio with NIFTY index

futures.

We studied the basis risk between S&P CNX NIFTY, S&P CNX 500 and NIFTY

Futures and find out the theoretical price which can be compare with the actual

futures price which gives us the basis data on which we applied the “t” test and

find out that basis risk is exist or not.




CHAPTER 1

INTRODUCTION AND

THEORETICAL BACKGROUND




Introduction to Derivatives

The evolution occurred in stages. The Chicago Board of Trade (CBOT), which

opened in 1848, is, to this day, the largest futures market in the world. The

general rules framed by CBOT in 1865 became a pacesetter for many other

markets. In 1870, the New York cotton exchange was founded.

The London metal exchange was established in 1877 and is now the leading

market in metal trading (both spot and forward). Thereafter many new futures

market were started. The first financial futures market was the international

monetary, founded in 1972 by the Chicago mercantile exchange. The London

international financial futures exchange followed this in 1982.

As already mentioned, some form of forward trading probably existed in India

also. The first organized forward markets came into existence in India in the late

19th and early 20th century in Calcutta (for jute and jute goods) and Mumbai (for

cotton).

Chronologically, India’s experience in organized forward trading is almost as long

as that of the United Kingdom, and certainly longer than many developed

nations. However, the tidal wave of price control, nationalization and state

intervention in markets, which swept through all economic policy making after

independence, led to a rapid decline in number of futures markets. Frequently

markets were closed due to the feeling that they were responsible for sudden

movements of price in the commodities.




Definition of Derivatives

Derivatives are the financial instruments, which derive their value from some

other financial instruments, called the underlying. The foundation of all

derivatives market is the underlying market, which could be spot market for gold,

or it could be a pure number such as the level of the wholesale price index of a

market price.

A derivative is a financial instrument whose value depends on the value of

other basic underlying variables.

John c hull

According to the Securities Contract (Regulation) Act, 1956, derivatives

include:

A security derived from a debt instrument, share, and loan whether

secured or Unsecured, risk instrument or contract for differences or any

other form of Security.

A contract, which derives its value from the prices or index of prices of

underlying securities.

Therefore, derivatives are specialized contracts to facilitate temporarily for

hedging which is protection against losses resulting from unforeseen price or




volatility changes. Thus, derivatives are a very important tool of risk

management. Derivatives perform a number of economic functions like price

discovery, risk transfer and market completion.

The simplest kind of derivative market is the forward market. Here a buyer and

seller write a contract for delivery at a specific future date and a specified future

price. In India, a forward market exists in the form of the dollar-rupee market. But

forward market suffers from two serious problems; counter party risk resulting in

comparatively high rate of contract noncompliance and poor liquidity.

Futures markets were invented to cope with these two difficulties of forward

markets. Futures are standardized forward contracts traded on an organized

stock exchange. In essence, a future contract is a derivative instrument whose

value is derived from the expected price of the underlying security or asset or

index at a pre-determined future date.

Types of Derivatives

• FORWARDS

• FUTURE

• OPTIONS

• SWAPS

One form of classification of derivatives is between commodity derivatives and

financial derivatives. Thus futures, option or swaps on gold, sugar, jute, pepper

etc are commodity derivatives.




While futures, options or swaps on currencies, gilt-edged securities, stock and

share stock market indices etc are financial derivatives.

PREREQUISITES FOR DERIVATIVES MARKET

There are five essential prerequisites for derivatives market to flourish in a

country.

a) Large market capitalization

At a market capitalization of near $1.5 trillion, India is well ahead of many other

countries where derivatives markets have succeeded.

b) Liquidity in the underlying

A few years ago, the total trading volume in India used to be around Rs-300

crores a day. Today, daily trading volume in India is around Rs-15000 crores a

day. This implies a degree of liquidity, which is around six times superior to the

earlier conditions. There is empirical evidence to suggest that there are many

financial instruments in the country today, which have adequate to support

derivative market.

c) Clearing house that guarantees trades




Counter party risk is one of the major factor recognized as essential for starting a

strong and healthy derivatives market. Trade guarantee therefore becomes

imperative before a derivatives market could start. The first clearinghouse

corporation guarantees trades have become fully functional from July 1996 in the

form of National Securities Clearing Corporation (NSCC). NSCC is responsible

for guaranteeing all open positions on the National Stock Exchange (NSE) for

which it does the clearing. Other exchanges are also moving towards setting up

separate and well-funded clearing corporations for providing trade guarantees

d) Physical infrastructure

India.s equity markets are all moving towards satellite connectivity, which allows

investors and traders anywhere in the country to buy liquidity services from

anywhere else. This telecommunications infrastructure, India.s capabilities in

computer hardware and software, will enable the establishment of computer

system for creation of derivatives markets. Setting up of automated trading

system as an experience with various prospective exchanges will also be

beneficial while setting up the derivative market.

e) Risk-taking capability and Analytical skills

India’s investors are very strong in their risk-bearing capacity and can cope with

the risk that derivatives pose. Evidence of the volumes traded on the capital

markets, which are akin to a futures market, is indicative of this capacity. In

contrast, in some other countries, investors simply lack the risk-bearing capacity

to sustain the growth of even the equity market. It is expected that such a barrier

will not appear in India.




On the subject of analytical skills, derivatives require a high degree of analytical

capability for many subtle trading strategies to pricing. India has an enormous

pool of mathematically literate finance professionals, who would excel in this

field. Lastly, an obvious advantage for the Indian market is that we have

enormous experience with futures markets through the settlement cycle oriented

equity which is not truly a spot market but a futures market (including concepts

like market-to-market margin, low delivery ratios, and last-day-of settlement

abnormalities in prices). We also have active futures markets on six

commodities. With this state of development of the capital markets it is felt that

there is no major hurdle left for the creation of development of the capital

markets. Hence on July 2, 1996 the SEBI board gave an in principal approval for

the launch of derivatives markets in India.

A) OPTIONS:

The concept of options is not new one. In Fact, options have been in use for

centuries. The idea of an option existed in ancient Greece and Rome. The

Romans wrote options on the cargo that were transported by their ship. In the

17th century, there was an active option markets in Holland. In fact, options were

used in a large measure in the .tulip bulb mania . of that century. However, in the

absence of mechanism to guarantee the performance of the contract, the refusal

of many put option writers to take delivery of the tulip bulb and pay the high

prices of the bulb they had originally agreed to, led to bursting of the bulb bubble

during the winter of 1637.A number of speculators were wiped out in the process.

In India, options on stocks of companies were illegal until 25th January 1995

according to sec. 20 of Securities Contracts (Regulation) Act, 1956. When




Securities Laws (Amendment) Act, 1956 deleted sec. 20, thus making the

introduction of options as legal act.

An options contract is an agreement between a buyer and a seller. Such a

contract confers on the buyer a right but not an obligation to buy or sell a

specified quantity of the underlying asset at a fixed price on or up to a fixed day

in the future on a payment of a premium to the seller. The premium paid by the

buyer to the seller is the price of an

option contract

Options on a futures contract have added a new dimension to future trading like

futures options provide price protection against adverse price move. Present day

options trading on the floor of an exchange began in April 1973. When the

Chicago Board of trade created the Chicago Board Options Exchange (CBOE)

for the sole purpose of trading Options on a limited number of NEW YORK

STOCK EXCHAGE listed equities

B) FORWARDS:

A forward is an agreement between two parties to exchange an agreed quantity

of asset at a specified future date at a predetermined price specified in the

agreements. The parties concerned agree the settlement date and price in

advance. The promised asset may be currency, commodity, instrument etc. It is

the oldest type of all the derivatives. The party who promises to buy but he

specified asset at an agreed price at a fixed future date is said to be in the .Long

position . and the party who promises to sell at an agreed price at a future date is

said to be in . short position..




C) FUTURES:

It is similar to the forward contract in all the respect. In fact, a future is a

standardized form of forward contract. A future is a contract or an agreement

between two parties to exchange assets / currency or commodity at a certain

future date at an agreed price. The trader who promises to buy is said to be in .

long position . and the party who promises to sell said be in .short position. .

Futures contracts are contracts specifying a standard volume of a particular

currency to be exchanged on a specific settlement date. A future contract is an

agreement between a buyer and a seller. Such a contract confers on the buyer

an obligation to buy from the seller, and the seller an obligation to sell to the

buyer a specified quantity of an underlying asset at a fixed price on or before a

fixed day in future. Such a contract can be for delivery of an underlying asset.

To eliminate counter party risk and guarantee traders, futures markets use a

clearing house which employs initial margin, daily market to market margin,

exposures limits etc. to ensure contract compliance and guarantee settlement

standardized futures contracts generate liquidity. In addition, due to these

instruments being traded on recognized exchange.s results in grater

transparency, fairness and efficiency. Due to these inherent advantages, futures

markets have been enormously successful in comparison with forward markets

all over the world The difference between forward contract and future is that

future is a standardized contract in terms of quantity, date and delivery. It is

traded on organized exchanges. So it has secondary markets. Future contract is




always settled daily, irrespective of the maturity date, which is called marking to

the market.

D) SWAP:

Swap is an agreement between two parties to exchange one set of financial

obligations with other. It is widely used throughout the world but is recent in India.

Swap may be interest swap or currency swaps.

Swaps give companies extra flexibility to exploit their comparative advantage in

their respective borrowing markets.

Swaps allow companies to focus on their comparative advantage in borrowing in

a single currency in the short end of the maturity spectrum vs. the long-end of the

maturity spectrum.

Swaps allow companies to exploit advantages across a matrix of currencies and

maturities




THEORETICAL BACKGROUND

Corporation in which individual investor place their money have exposure to

fluctuation of all kinds of financial price, as a natural by product of their operation.

Financial prices include foreign exchange rate, interest rates, commodity prices

and equity prices. The effect of changes in prices reported on earnings is

overwhelming.

Hedging is a way of reducing some of the risk involved in holding an investment.

There are many financial instruments which are used in hedging. In considering

potential application of index futures, it is clear that in nearly every case a cross

hedge is involved. That is the stock position that is being hedge is different from

the underlying portfolio of index contract. This means that the return and risk for

an index futures hedge will depend upon the behavior of “Basis” i.e., the

difference between the futures prices and cash prices. Hedging a position in

stock will necessarily expose it to some measure of Basis risk – risk that the

change in future price over time will not track exactly the value of cash position.

Future prices and the factors that determine these prices will ultimately influence

every user of the market. Futures market prices reflect economically important

relationship to other prices as well. For example, the futures prices for delivery of

gold in 3 months must be related to the spot price for immediate delivery. The

spot price is also known as cash price or current price. The difference between

the cash price and the futures price is called the Basis. Basis is an important

concept in futures contract. Similarly, the future prices are for delivery of gold in

six months. This price difference of the futures on the same commodity is an

intra-commodity spread. The time spread can also be an economically important

variable in futures contracts. The relation between futures prices and expected




future spot prices is so strong, that some market observers believe that they

must be, or at least should be equal. The price for storing the goods underlying

the futures contract helps determine the relationship among future prices and the

relationship between the future price and the spot prices. Thus the future pricing

issues like the bases,the spreads, the expected future spot price and the cost of

storage are interconnected

Basis and Spreads

What is Basis?

The basis is the current cash prices of a particular commodity at a particular

location minus the prices of particular future contract for the same commodity.

Basis: Current Cash Price – Future Price

If the same commodity had two prices in two different markets, a trader could buy

the commodity in cheaper market and sell it in the market with higher price,

thereby making an arbitrage profit. So the basis is calculated in considering

futures prices may differ, depending upon the geographic location of the spot

price that is used to calculate the basis.

Future markets can exhibit a pattern of either normal or inverted prices. Prices for

more distant futures are higher than for nearby futures in a normal market.

Distant futures prices are lower than the prices for contracts near to expiration in

an inverted market. This is so particularly in agricultural products in view of

seasonal production and drastic reduction in price due to heavy supply of




products in that season. This situation may also happen in case of other

commodities including securities also in view of political and other environmental

factors. Traders believe that understanding these seasonal and environmental

factors can be very beneficial for speculation and hedging. The futures prices

and the spot price of gold must be the same. The basis must be zero, again

subject to the disperancy due to transaction cost.

Spreads

Spreads refers to difference in prices of two futures contracts. There are two

types of spreads viz., intra-commodity spreads and inter- commodity spreads.

The difference in price between two future contracts of different maturity dates on

the same commodity is known as intra-commodity spread. An intra –commodity

spread is the difference for two different commodities with the same maturity. An

understanding of spread relationship is essential to earn speculative profits.

Though certain general principles may help to earn profits, considerable

knowledge in a particular commodity itself, will enable the trader to make use of

spread relationship.

What is a stock index futures contract?

Stock index futures are traded in terms of number of contracts. Each contract is

to buy or sell a fixed value of the index. The value of the index is defined as the

value of the index multiplied by the specified monetary amount. In the S&P 500

futures contract traded at the Chicago Mercantile Exchange (CME), the contract

specification states:

1 Contract = $250 * Value of the S&P 500




If we assume that the S&P 500 is quoting at 1,000, the value of one contract will

be equal to $250,000 (250*1,000). The monetary value -- $250 in this case -- is

fixed by the exchange where the contract is traded.

Mechanics of futures trading

Like most other financial instruments, futures contracts are traded on recognised

exchanges. In India, both the NSE and the BSE plan to introduce index futures in

the S&P CNX Nifty and the BSE Sensex. The operations are similar to that of the

stock market, the exception being that, in index futures, the marking-to-market

principle is followed, that is, the portfolios are adjusted to the market values on a

daily basis.

Depending on the position of the portfolio, margins are forced upon investors.

The other important aspect of index futures is that the contracts are settled on a

cash basis. This means it is impossible to make actual delivery of the index. The

difference between the cash and the futures index on the date of settlement is

the profit/loss for the players.

Why buy index futures?

What is the rationale behind using index futures? Academic literature on the

subject shows that, in some cases, the introduction of the index futures has

actually reduced the volatility in the underlying index. The theory behind this is

interesting.

Technical analysts thrive on their ability to predict the movement of the broad

market indices. However, as they cannot trade the index, the normal practice is




However, index futures provide investors an efficient and cost-effective means of

hedging and significant improvements in market timing. The introduction of index

futures need not necessarily be bad for the capital market, so long as proper

checks are in place to prevent unwarranted speculation.

Meaning and definitions of hedging

The first rule of hedging is ‘do no harm.’ Like no-fat cream cheese, there are

some things that remove more good stuff than bad. A good hedge diminishes

volatility proportionally more than the return, so that if the hedge reducesannualized volatility by X%, it should reduce annualized return by no more than

X%.

The best way to understand hedging is to think of it as insurance. When people

decide to hedge, they are insuring themselves against a negative event. This

doesn't prevent a negative event from happening, but if it does happen and

you're properly hedged, the impact of the event is reduced. So, hedging occurs

almost everywhere, and we see it everyday. For example, if you buy house

insurance, you are hedging yourself against fires, break-ins or other unforeseen

disasters.

Portfolio managers, individual investors and corporations use hedging techniques

to reduce their exposure to various risks. In financial markets, however, hedging

becomes more complicated than simply paying an insurance company a feeevery year. Hedging against investment risk means strategically using

instruments in the market to offset the risk of any adverse price movements. In

other words, investors hedge one investment by making another.




Technically, to hedge you would invest in two securities with negative

correlations. Of course, nothing in this world is free, so you still have to pay for

this type of insurance in one form or another.

Although some of us may fantasize about a world where profit potentials are

limitless but also risk free, hedging can't help us escape that hard reality of the

risk-return tradeoff. A reduction in risk will always mean a reduction in potential

profits. So, hedging, for the most part, is a technique not by which you will make

money but by which you can reduce potential loss. If the investment you are

hedging against makes money, you will have typically reduced the profit that you

could have made, and if the investment loses money, your hedge, if successful,

will reduce that loss.

How Do Investors Hedge?

For the most part, hedging techniques involve using complicated financial

instruments known as derivatives, the two most common of which are options

and futures. We're not going to get into the nitty-gritty of describing how these

instruments work, but for now just keep in mind that with these instruments you

can develop trading strategies where a loss in one investment is offset by a gain

in a derivative.

.

Keep in mind that because there are so many different types of options and

futures contracts an investor can hedge against nearly anything, whether a

stock, commodity price, interest rate, or currency.




One reason why companies attempt to hedge these price changes is because

they are risks that are peripheral to the central business in which they operate.

For example, an investor buys the stock of a pulp-and-paper company in order to

gain from its management of a pulp-and-paper business. She does not buy the

stock in order to take advantage of a falling Canadian dollar, knowing that the

company exports over 75% of its product to overseas markets. This is the

insurance argument in favour of hedging. Similarly, companies are expected to

take out insurance against their exposure to the effects of theft or fire.

By hedging, in the general sense, we can imagine the company entering into a

transaction whose sensitivity to movements in financial prices offsets the

sensitivity of their core business to such changes. As we shall see in this article

and the ones that follow, hedging is not a simple exercise nor is it a concept that

is easy to pin down. Hedging objectives vary widely from firm to firm, even

though it appears to be a fairly standard problem, on the face of it. And the

spectrum of hedging instruments available to the corporate Treasurer is

becoming more complex every day.

Another reason for hedging the exposure of the firm to its financial price risk is to

improve or maintain the competitiveness of the firm. Companies do not exist in

isolation. They compete with other domestic companies in their sector and with

companies located in other countries that produce similar goods for sale in the

global marketplace. Again, a pulp-and-paper company based in Canada has

competitors located across the country and in any other country with significant

pulp-and-paper industries, such as the Scandinavian countries.

Companies that are the most sophisticated in this field recognize that the

financial risks that are produced by their businesses present a powerful

opportunity to add to their bottom line while prudently positioning the firm so that




it is not pejoratively affected by movements in these prices. This level of

sophistication depends on the firm's experience, personnel and management

approach. It will also depend on their competitors. If there are five companies in a

particular sector and three of them engage in a comprehensive financial risk

management program, then that places substantial pressure on the more passive

companies to become more advanced in risk management or face the possibility

of being priced out of some important markets. Firms that have good risk

management programs can use this stability to reduce their cost of funding or to

lower their prices in markets that are deemed to be strategic and essential to the

future progress of their companies.

Most importantly, hedging is contingent on the preferences of the firm's

shareholders. There are companies whose shareholders refuse to take anything

that appears to be financial price risk while there are other companies whose

shareholders have a more worldly view of such things. It is easy to imagine two

companies operating in the same sector with the same exposure to fluctuations

in financial prices that conduct completely different policy, purely by virtue of the

differences in their shareholders' attitude towards risk.

The hedging problem

The core problem when deciding upon a hedging policy is to strike a balance

between uncertainty and the risk of opportunity loss. It is in the establishment of

balance that we must consider the risk aversion, the preferences, of the

shareholders. Make no mistake about it. Setting hedging policy is a strategic

decision, the success or failure of which can make or break a firm.




Consider the example of the Canadian pulp-and-paper company from before,

75% of whose product is sold in US dollars to customers located all over the

world. The US dollar here is called the price of determination because all sales of

pulp-and-paper are denominated in US dollars.

They close a deal for US$10 million worth of product and they know that in one

month's time they will receive payment into their US dollar accounts. However,

they understand that from the inception of the contract which binds them to have

receivables in US dollars in one month's time they are exposed to changes in the

rate of exchange for the Canadian dollar against the US dollar.

Immediately, they are faced with a problem. As a Canadian company, they will

have to repatriate those US dollars at some point because they have decided

that foreign exchange risk is not something that they are prepared to carry as it is

deemed it to be peripheral to their core business.

The problem has two dimensions: uncertainty and opportunity.

If they do not hedge the transaction in any way, they do not know with any

certainty at what rate of exchange they can exchange the US$10 million when it

is delivered. It could be at a better rate or at a worse rate than the rate prevailingcurrently for exchange of that amount in one month's time.




Let's call the prevailing spot rate, for argument's sake, 1.5300 and the prevailing

one month forward outright rate at which they could hedge themselves 1.5310.

If they do enter into a forward contract in which they obligate themselves to buy

Canadian dollars and sell US dollars for delivery on the same date as the

delivery date on their pulp-and-paper contract, they have removed this

uncertainty. They know without any question at what rate this exchange will be. It

will be 1.5310.

But, they have now taken on infinite risk of opportunity loss. If the Canadian

dollar weakens because of some unforeseen event and in one month's time the

prevailing spot rate turns out to be 1.5600, then they have foregone 290,000

Canadian dollars. This is their opportunity loss.

Are there instruments that address both certainty and opportunity loss?Fortunately, there are. They are called derivatives or derivative products. Most

financial institutions make markets in a panoply of risk management solutions

involving derivative products. Some of them come as stand-alone solutions and

others are presented as packages or combinations.

A derivative product is a financial instrument whose price depends indirectly onthe behaviour of a financial price.




For example, the price of a foreign exchange option on the Canadian dollar in

which our company had the right but not the obligation to buy Canadian dollars

and sell US dollars at a pre-set strike price will vary on a day-to-day basis with

the movement in the Canadian dollar/US dollar exchange rate. If the Canadian

dollar gets stronger, the Canadian dollar call becomes more valuable. If the

Canadian dollar gets weaker, the Canadian dollar becomes less valuable.

Instead of entering into a forward contract to buy Canadian dollars, the pulp-and-

paper company could purchase a Canadian dollar call struck at 1.5310 for a

premium from one of its financial institution counterparties. Doing so reduces

their certainty about the rate at which they will repatriate the US dollars but it

limits their worst case in exchange for allowing them to enjoy potential

opportunity gains, again conditioned by the premium they have paid.

Derivatives just like any other economic mechanism are best thought of in terms

of tradeoffs. The tradeoffs here are between uncertainty and opportunity loss.

However, a Canadian dollar call is only one of the possible risk management

solutions to this problem. There are dozens of possible instruments, each of

which has a differing tradeoff between uncertainty and opportunity loss, that the

pulp-and-paper company could use to manage this exposure to changes in the

exchange rate.

The key to hedging is to decide which of these solutions to choose. Hedging is

not just about putting on a forward contract. Hedging is about making the best




possible decision, integrating the firm's level of sophistication, systems and the

preferences of their shareholders.

Future articles will discuss in depth the nature of some of these alternative

solutions and the ways in which firms approach these other instruments.

Hedging objectives

.

Earlier, we noted that a hedge is a financial instrument whose sensitivity to a

particular financial price offsets the sensitivity of the firm's core business to that

price. Straightaway, we can see that there are a number of issues that present

themselves.

First, what is the hedging objective of the firm?

Some of the best-articulated hedging programs in the corporate world will choose

the reduction in the variability of corporate income as an appropriate target. This

is consistent with the notion that an investor purchases the stock of the company

in order to take advantage of their core business expertise.

Other companies just believe that engaging in a forward outright transaction to

hedge each of their cross-border cash flows in foreign exchange is sufficient to

deem themselves hedged. Yet, they are exposing their companies to untold

potential opportunity losses. And this could impact their relative performance

pejoratively.

Second, what is the firm's exposure to financial price risk?

It is important to measure and to have on a daily basis some notion of the firm's

potential liability from financial price risk. Financial institutions whose core




business is the management and acceptance of financial price risk have whole

departments devoted to the independent measurement and quantification of their

exposures. It is no less critical for a company with billions of dollars of

internationally driven revenue to do so.

There are three types of risk for every particular financial price to which the firm

is exposed.

Transactional risks reflect the pejorative impact of fluctuations in financial prices

on the cash flows that come from purchases or sales. This is the kind of risk we

described in our example of the pulp-and-paper company concerned about their

US$10 million contract. Or, we could describe the funding problem of the

company as a transactional risk. How do they borrow money? How do they

hedge the value of a loan they have taken once it is on the books?

Translation risks describe the changes in the value of a foreign asset due to

changes in financial prices, such as the foreign exchange rate.

Economic exposure refers to the impact of fluctuations in financial prices on the

core business of the firm. If developing markets economies devalue sharply while

retaining their high technology manufacturing infrastructure, what effect will this

have on an Ottawa-based chip manufacturer that only has sales in Canada? If it

means that these countries will flood the market with cheap chips in a desperate

effort to obtain hard currency, it could mean that the domestic manufacturer is in

serious jeopardy.

Third, what are the various hedging instruments available to the corporate

Treasurer and how do they behave in different pricing environments?

When is it best to use which instrument is the question the corporate Treasurer

must answer. The difference between a mediocre corporate Treasury and an

excellent one is their ability to operate within the context of their shareholder-

delineated limits and choose the optimal hedging structure for a particular




exposure and economic environment. Not every structure will work well in every

environment. The corporate Treasury should be able to tailor the exposure using

derivatives so that it fits the preferences and the view of the senior management

and the board of directors.

A stock trader believes that the stock price of FOO, Inc., will rise over the next

month, due to this company's new and efficient method of producing widgets. He

wants to buy FOO shares to profit from their expected price increase. But FOO is

part of the highly volatile widget industry. If the trader simply bought the shares

based on his belief that the FOO shares were underpriced, the trade would be a

speculation.

Since the trader is interested in the company, rather than the industry, he wants

to hedge out the industry risk by short selling an equal value (number of shares ×

price) of the shares of FOO's direct competitor, BAR. If the trader were able to

short sell an asset whose price had a mathematically defined relation with FOO's

stock price (for example a call option on FOO shares) the trade might be

essentially riskless and be called an arbitrage. But since some risk remains in the

trade, it is said to be "hedged."

The first day the trader's portfolio is:

• Long 1000 shares of FOO at $1 each

• Short 500 shares of BAR at $2 each

(Notice that the trader has sold short the same value of shares.)




On the second day, a favorable news story about the widgets industry is

published and the value of all widgets stock goes up. FOO, however, because it

is a stronger company, goes up by 10%, while BAR goes up by just 5%:

• Long 1000 shares of FOO at $1.10 each $100 profit

• Short 500 shares of BAR at $2.10 each $50 loss

(In a short position, the investor loses money when the price goes up.)

The trader might regret the hedge on day two, since it reduced the profits on the

FOO position. But on the third day, an unfavorable news story is published about

the health effects of widgets, and all widgets stocks crash -- 50% is wiped off the

value of the widgets industry in the course of a few hours. Nevertheless, since

FOO is the better company, it suffers less than BAR:

Value of long position (FOO):

• Day 1 $1000

• Day 2 $1100

• Day 3 $550 => $450 loss

Value of short position (BAR):

• Day 1 $1000

• Day 2 $1050




• Day 3 $525 => $475 profit

Without the hedge, the trader would have lost $450. But the hedge - the shortsale of BAR - gives a profit of $475, for a net profit of $25 during a dramatic

market collapse

Natural hedges

Many hedges do not involve exotic financial instruments or derivatives. A natural

hedge is an investment that reduces the undesired risk by matching cash flows,

i.e. revenues and expenses. For example, an exporter to the United States faces

a risk of changes in the value of the U.S. dollar, and could choose to open a

production facility in that market to match its expected sales revenue to its cost

structure. Another example is a company that opens a subsidiary in another

country and borrows in the local currency to finance its operations, even though

the local interest rate may be more expensive than in its home country: by

matching the debt payments to expected revenues in the local currency, the

parent company has reduced its foreign currency exposure.

Similarly, an oil producer may expect to receive its revenues in U.S. dollars, but

face costs in a different currency; it would be applying a natural hedge if it agreed

to, for example, pay bonuses to employees in U.S. dollars.




One of the oldest means of hedging against risk is the purchase of protection

against accidental property damage or loss, personal injury, or loss of life. See

Insurance.

Contract for differences

A Contract for Differences (CfD) is a two way hedge or swap contract that allows

the seller and purchaser to fix the price of a volatile commodity. For instance,

consider a deal between an electricity producer and an electricity retailer whoboth trade through an electricity market pool. If the producer and the retailer

agree to a strike price of $50 per MWh, for 1 MWh in a trading period, and if the

actual pool price is $70, then the producer gets $70 from the pool but has to

rebate $20 (the "difference" between the strike price and the pool price) to the

retailer. Conversely, the retailer pays the difference to the producer if the pool

price is lower than the agreed upon contractual strike price.

In effect, the pool volatility is nullified and the parties pay and receive $50 per

MWh. However, the party who pays the difference is "out of the money" because

without the hedge they would have received the benefit of the pool price

Currency hedging is used both by financial investors to parse out the risks they

encounter when investing overseas, as well as by non-financial actors in the

global economy for whom multi-currency activities is a necessary evil rather than

a desired state of exposure. For example, cost of labor variables dictate that

much of the simple commoditized manufacturing in the global economy today

goes on in China and south-east Asia (Taiwan, Philippines, Vietnam, Indonesia,

etc.). The cost benefit of moving manufacturing to outsource providers outweighs

the uncertainties of never having done business in foreign countries, so many

businesses are jumping into the fray and becoming part of the globalization trend




of moving manufacturing operations overseas. The benefits of doing this

however, come with numerous risks that were never a problem when

manufacturing was done at home--among them currency risk.

If your cost of manufacturing goods in another country is denominated in a

currency other than the one that you sell the finished goods in, there is the risk

that the currency "volatility" alone may destroy the margin between what you pay

to produce your product, and what you collect when you sell it (note you may be

selling your product in a foreign country too, so you can hedge against the

currency risk on this side as well!). So when you convert all costs on the

production side, and all sales receipts from the retail side, back into your home

currency, you may be alarmed to find that your profits have diminishedsignificantly, or disappeared altogether. That's currency risk-- it is germane to

doing business globally, but entirely independent of your specific business or

products. Currency hedging then, is the insurance you can purchase to limit the

impact this unpredictable risk has on your business, the same way Fire or

Hurricane insurance protects your physical premises from unexpected events

beyond your control.

Currency hedging is not always available, but is readily found at least in the

major currencies of the world economy, the growing list of which qualify as major

liquid markets beginning with the "Major Eight" (USD, GBP, EUR, JPY, CHF,

HKD, AUD, CAD), which are also called the "Benchmark Currencies", and

expands to include several others by virtue of liquidity. The currencies beyond

the Major 8 can most reliably be identified by checking to see which are included

within the "Continuous-Linked Settlement Bank" "(CLS Bank)", which handles a

growing percentage of the globe's daily settlement volume between currencies.

Currency hedging, like many other forms of financial hedging, can be done in two

primary ways, with standardized contracts, or with customized contracts (also

known as over-the-counter or OTC).




The financial investor may be a hedge fund that decides to invest in a company

in, for example, Brazil, but does not want to necessarily invest in the Brazilian

currency. The hedge fund can separate out the credit risk (i.e. the risk of the

Company defaulting), from the currency risk of the Brazilian Real by "hedging"

out the currency risk. In effect, this means that the investment is effectively a

USD investment, in Brazil. Hedging allows the investor to transfer the currency

risk to someone else who does want a position in the currency. The hedge fund

has to pay this other investor to take on the currency exposure, similar to insuring

against other types of events.

As with other types of financial products, hedging may allow economic activity to

take place that would otherwise not have been possible (as a loan, for example,may allow an individual to purchase a home that would be "too expensive". The

increased investment is assumed in this way to raise economic efficiency.

Constructing the hedge portfolio

The dealer will then take this analysis of the behavioural characteristics of the

swap portfolio and he will construct a hedging portfolio using one or more

financial instruments in order to offset those aspects of the risk that he is

unhappy carrying. Note that the dealer will not close out all of the aspects of the

risk.

Why will the dealer only partially hedge the swaps portfolio?

Hedging costs money. The main benefit of hedging activity is to reduce the risk of

the portfolio. This benefit must be compared to the hedging cost. If the marginal

benefit of reducing the risk with an individual transaction is less than its marginal

cost, it is not worthwhile to hedge that risk.




Another reason for not completely hedging the swaps portfolio is the fact that the

dealer may carry a proprietary position in one or more aspects of the risk. If, for

example, he thinks that interest rates are going to fall in the 2-year to 3-year

bucket, he may be happy to continue received fixed interest payments for that

period. If he is correct, he will make money on a mark-to-market basis that he

can realize by hedging the position at a preferable level.

Floating rate cash flow management

One of the more difficult aspects of managing a swap portfolio is managing the

short-term cash flows or the floating rate cash flows. There are two problems that

confront the dealer.

First, there may be mismatches in the timing of short-term cash flows.

Consider a hedge that was entered into two years ago to hedge a two year fixed-

floating plain vanilla interest rate swap where the hedge transaction took place aweek after the initial customer transaction. Unless the dealer matched the dates

precisely at the time he conducted the hedge transaction, there will be a one-

week mismatch of flows. Matching the dates may have cost extra money in terms

of the market prices at the time of transaction making it too expensive to match

the timing of the cash flows. Some people might argue that one week is not very

much of a difference. That is no way to run a business. To paraphrase an old

saying, ten grand here and one hundred grand there and pretty soon you're

talking about some real money.

Second, there may be mismatches in the type of index used to hedge.




Consider a swap in which the floating rate index is the 3-month US Bankers'

Acceptance rate. If the best swap available at the time is the 3-month US LIBOR

(London Interbank Offered Rate for US dollars), then there is an index mismatch

risk. If the correlation between these two indices changes (and correlation

between financial indices is rarely stable), then the swap portfolio is exposed to

refunding risk.

One way for the commercial bank to hedge its floating rate cash flows is to

establish a separate book dedicated to hedging such risks, one which

participates actively in the futures markets such as the IMM Eurodollar market

and one which takes aggressive positions in short-term interest rates.

An alternative might be to pay the hedging costs necessary for closing out the

mismatches. This can get expensive. With the increased commoditization of

global derivatives markets, dealers are losing much of their pricing edge, a

phenomenon that makes paying for outside hedging more difficult.

By giving an appreciation for the way swaps dealers manage their combined

portfolio risk, this article has identified some of the key types of risk in interest

rate swaps and interest rate products, generally.

EXAMPLE

Portfolio managers prefer futures to options to hedge their market risk. Why? If

you buy futures, you have to pay a margin, which is adjusted daily for the

gains/losses that you make on your futures position. You, therefore, do not incur

any cost for buying futures. This is quite unlike options, where you have to pay a

premium to buy calls and puts. This premium is a cost to the call/put buyer.




Now, consider a fund that has portfolio worth Rs 100 crore. Suppose the fund

manager sells Nifty futures contract at 1070. If the Nifty futures falls to 1044, the

fund will generate profits from the futures contract.

The profit will be 1070 minus 1044 times the number of futures contracts. This

profit will help reduce the losses that the fund will incur because of the fall in

price of stocks in its portfolio.

The most important step in portfolio hedging is the hedge ratio. This ratio tells the

fund manager how many contracts to buy to minimise the portfolio risk.

The fund manager may sometimes choose to hedge only part of the portfolio

because of the associated costs.

Average annual volatility comparison

Sensex or Nifty-35-45%

Govt Sec Index-5-10%

Gold -12-18%

Silver-15-25%

Cotton-10-12%

Oil seeds -15-20%

What is Risk Management?




In general no risk can be eliminated but still one can try to avoid it by transferring

someone.

Risk Management

Transferring the risk to some one who can handle it better or Transfer the risk to

some one who has the appetite for risk Financial derivatives are used to hedge

the exposure to market risk Hedgers transfer their risk to speculators who are

willing to assume the risk

Commodities are less volatile compared to stock market The determinants of

volatility are different for capital market and commodity markets

EXAMPLE

For example an investor has 1000 RELIANCE in cash market & he wants to

hedge the risk of adverse price movement ,he can sell the reliance futures or the

index futures so that if the price are going down he can lose in cash market but at

the same time he can gain in the futures markets .……..

A cotton hedge –an example

Two varieties of cotton are available for trading on NCDEX –J-34 (short

staple) and S-6 (long staple)




Suppose, a farmer in Andhra Pradesh producing Buny/ Brahma variety

(extra long staple) wishes to hedge on NCDEX

Net gain = Rs 1870 – Rs 1620 = Rs 250

Thus, we see that the farmer gains Rs. 250/-(per contract) by hedging at

NCDEX.

The loss in the spot market is notional.

For hedging to be effective, two things are necessary.

The futures and spot price for S-6 should move together Also, the spot price for

S-6 and Brahma / Buny should also move together.




Basis

Basis is usually quoted as a premium or discount i.e, the cash price as a

premium or discount to the futures price.

For example cash price of the XYZ share on 31-7-98 at Madras Stock Exchange

is Rs.400 and the 31.12.98 futures price would be Rs.440, at the Madras Stock

Exchange XYZ share basis is Rs.40.This is commonly quoted as 40 under as the

cash price is Rs.40 under the December’98 futures price. The basis will be

constant, if the futures and cash prices change by the same amount. Such a

hedge is called a ‘Perfect Hedge ’ as it eliminates all price risk.

The basis is said to be narrowing when it moves towards zero line. It does

mean that the absolute difference between cash price and futures prices become

smaller. A widening of the basis occurs the basis moves away from the zero line

and the difference of prices increases. A narrowing or widening of the basis

results in profit or loss for hedgers depending on the type of hedge (long or short)

and on market conditions. A short hedger is said to be the long basis and the

long hedger is said to be the short basis. A narrowing of the basis, regardless of

the general price trend, benefits the short hedger( he is long the basis) and a

widening of the basis benefits the long hedger( he is short the basis) in a carry

market is also known as Contango market.

In a backwardation market (or an inverted market) a narrowing of the basis

benefits the long hedger, and a widening of the basis benefits the short hedger,

just the reverse of the contango market. Variation in basis often follows a

seasonal pattern which reflects the changing relationships between demand for

and supply of a commodity. Hedgers should recognize this seasonality. They




may be able to benefit when the market switches from backwardation into

contango and vice versa.

A loss in one market means a profit in the other, as long as opposite

positions are maintained, one in each market. Prices in both markets run parallel

because both respond to the same stimuli of supply and demand. The rule of

thumb is rooted in the relationship of cash-to-futures prices called the “basis”.

The basis widens or narrows as the cash and futures prices fluctuate

independently. It is this change that provides the foundation for hedging.

To a certain extent, selling hedges are matched one-for-one by buying

hedges. However, in actual practice, seldom are two parties ready at precisely

the same moment to initiate a futures contract. And to further complicate the

trading, the quantities of the two parties may differ. Or both may want to sell or to

buy at the same time. Some hedgers therefore may not find others whose

interests are in hedging. This is where the speculator comes in.

For the most part, the speculator carries the hedging load by assuming

the risk and taking the opposite side of the contract. The speculator bridges the

gap between the buying and selling hedgers. Further, a hedger uses many

speculators in the market as underwriters and the contract as insurance policy.

The risk is shifted from one person’s shoulders and distributed in smaller parts

among the many speculators.

Most business persons are not in business to speculate on the rise or

fall of commodity prices. To protect their profit margin , therefore, against a

decline in the price of the actual commodity while it is in their possession ,they




hedge by selling the number of futures contracts approximately equivalent to the

amount of actual held. Selling hedges are used for basically 3 purposes.

To protect inventories of commodities not covered by actual sales or by sales of

its products.

To protect, to earn, an expected carrying charge on commodities

stored to protect, or to ensure, a given price for prospective or estimated

production of commodities.

Short Hedge with Zero Basis Risk

A fertilizer company of Andhra Pradesh which has large inventory on 1,may’98,

enters into an agreement to supply fertilizers to the farmers on 3 rd Aug’98 at a

price equal to the cash price that exists in Andhra Pradesh on this date. Thus the

company’s selling price in August is unknown in May. For example, the cost of

fertilizer per quintal is Rs.300 on 1 May’98 and the cost of inventory is Rs.20 per

quintal to carry until 3rd Aug’96. The company would earn a profit of Rs.30, if the

fertilizer price would be Rs.350 on 3rd Aug’98. The company would incur loss of

Rs.20, if the fertilizer price would be Rs.300 per quintal on 3rd Aug ’98. The

company can protect its profit margin by the short hedge (by entering into futures

contracts) in view of the variability of the net revenue is zero.

Long Hedge in Wheat Futures




Short Hedge with Basis Risk

When futures prices increase more than that of cash prices due to widening in

the basis, the hedger incurs a larger loss on his short futures positions. When the

basis is assumed to narrow, futures prices fall by more than cash prices. The

loss incurred on the distributor’s cash position is more than offset by the profit on

the futures position. Therefore, the net profits are considerably higher. As such,

changes in the basis can dramatically alter hedging results from what they would

be in the absence of basis risk. Hence, the strategy in constructing a hedge

would be to minimize basis risk in order to make the outcome of the hedge more

predictable.




Buying hedge

A buying hedge is intended to protect against an advance in the price of the cash

commodity (or its products) that had already been sold at a specific price; but not

yet purchased. Exporter and manufacturers commonly sell commodities or their

products at an agreed –upon price for forward delivery. The forward delivery is




said to be uncovered if the commodity is not on hand. The secret of success in a

buying hedge is that initiating a futures position should coincide as closely as

possible with the signing of a contract for actual forward sales. Timing is very

important.

Buying hedges are used, basically for three purposes; each of these is discussed

below:

To protect uncovered forward sales of a commodity or its products.

To replace inventory at a lower cost.

To maintain prices on stable –price products.

Long Hedge with Zero Basis Risk

The wholesaler of rice has a long term supply contract on 1 March’98 that

requires him to deliver 50,000 tonnes of rice on 15th October’98 to retailers at Rs.

11000 per tonne to the retailers. The wholesaler discovers on 15 th Oct’98 that he

does not have enough stock to cover this agreement in view of unseasonal

factors. He will, therefore, have to acquire additional stock, to meet his supply

obligations. The 1 March’98 price cash price was Rs.9000 per tonne. The 15th

Oct’98 cash price is Rs.12000per tonne.

There are two alternatives. The first one is purchase price on 1 March’98

at Rs.9000 and incurs carry cost @ Rs.500 per tonne and delivers it at Rs.11000

on 15th Oct’98. In this case his net profit is Rs.11000- Rs.9500 (Rs.9000+500)

Rs.1500 per tonne. The second strategy is promised on the belief that the rice

prices will fall between 1 March and 15 th Oct when cash prices are assured to be




lower. This will result for even greater profits, if the prices on 15 th Oct’98 are

lower than Rs.9000. The risk, of course, is that prices will rise instead of fall, in

which case he may incur a loss. The wholesaler does not want to be exposed to

this risk nor does he want to purchase rice now and carry it. Therefore he settles

on a third strategy i.e, a long hedge in rice. The following two examples describe

the result of such a hedging strategy under the assumption that the basis does

not change. The basis is Rs.11000-9000=2000. In case 1 cash prices fall to

Rs.8500, whereas in case 2, they rise to Rs.12000 and the hedge succeed in

locking profit in both the cases.

Long Hedge with Basis Risk

If the constant basis is not taken as an assumption, unanticipated changes in the

basis can cause substantial variation in hedging results for either long or short

hedgers.

• The future contract standardized size units do not match the cash

position quantity

• Use a combination of regular size futures and mini contracts to reach

a futures position as close as possible to the cash position

• An over hedged occurs when futures quantity exceeds the cash

quantity

• An under hedged occurs when the cash position exceeds the future

quantity




COST OF HEDGING

• Lack of liquidity in the market resulting in impact cost

• Low liquidity results in higher volatility

• Margin finance

• Margins are based on volatility

• The real cost of hedging is the finance cost of margins

• Margins could range from 5% to 50%




CHAPTER 2

REVIEW OF LITERATURE




Basis Risk: Measurement and Analysis of Basis Fluctuations for Selected

Livestock Markets

Philip Garcia; Raymond M. Leuthold; Mohamed E. Sarhan

American Journal of Agricultural Economics, Vol. 66, No. 4. (Nov., 1984), pp.

499-504.

This study examines the unsystematic, or random, fluctuations of the hog and

cattle basis over time in several Midwest markets. They found that unanticipated

basis changes can reduce the ability of futures markets to transfer risk and can

affect income levels of producers and market participants.

Taxes and the Pricing of Stock Index Futures

Bradford Cornell; Kenneth R. French

The Journal of Finance, Vol. 38, No. 3. (Jun., 1983), pp. 675-694.

This paper examines the pricing of stock index futures contracts. Under the

standard assumption that taxes are levied on both realized and unrealized capital

gains, we find that the futures price will differ from the stock price for two

reasons. First, payment for the stock is required today while the futures payment

is deferred until the contract matures. Second, the futures trader does not receive

the dividends that are paid to the stockholder.

Cross Hedging

Ronald W. Anderson; Jean-Pierre Danthine

The Journal of Political Economy , Vol. 89, No. 6. (Dec., 1981), pp. 1182-1196.

We have ignored the fact that futures contracts are standardized as to quantity

and must be traded in integer multiples. For a small user this discreteness is a




serious concern and nearly eliminate the possibility of multiple cross hedges.

Even for the large hedger the discreteness of futures markets implicitly may limit

the number of markets that should be considered in the portfolio.




Statement of problem

When the portfolio is hedged with the help of index futures, the future prices will

not track exactly the value of cash position. There are some sources of basis risk

prevalent in the market which causes the poor performance of hedge.

RESEARCH OBJECTIVES

• To understand the use and analyze the performance of index futures in

hedging.

• To know the basis risk and sources of basis risk.

• To analyze effect of different sources of basis risk.




Study Design

a) Study Type:

The study type is analytical, quantitative and historical. Analytical because

facts and existing information is used for the analysis, Quantitative as

relationship is examined by expressing variables in measurable terms and also

Historical as the historical information is used for analysis and interpretation.

b) Study population:

Population is the entire stock market and daily closing of NIFTY Index,

S&P CNX 500 and NIFTY Futures.

c) Sampling frame:

Sampling Frame would be Indian stock market and index futures markets.

d) Sample:

Sample chosen is daily closing values of NIFTY Index, S&P CNX 500 and

NIFTY Futures from 01-07-2000 to 31-3-2007.

e) Sampling technique:

Deliberate sampling is used because only particular units are selected

from the sampling frame. Such a selection is undertaken as these units represent

the population in a better way and reflect better relationship with the other

variable.




SAMPLE SIZE AND DATA SOURCES

The data will be the daily closing price of NIFTY, S&P CNX 500 & closing prices

of NIFTY index futures from.

SAMPLE PERIDOD

1st of July, 2000 to 31st March 2007




Analysis and Interpretation

Steps followed in the analysis-

• The data is collected for-

i) NIFTY Index

ii) NIFTY Futures

iii) S&P CNX 500.

• Period of data collection is 1st July,2000 to 31st march,2007

• The data is converted into log naturals format to way out any spurious

correlations within the data sets.

• Then the data is tested for its stationarity using Augmented Dickey fuller

test




TEST OF STATIONARITY

Dickey-fuller Test for unit root:

Dickey fuller statistic test for the unit root in the time series data r t is regressed

against r t-1 to test for unit root in a time series random walk model.

This is given as:

r t = ρ r t-1 + u t

if ρ is significant equal to 1, then the stochastic variable r t is said to be having unit

root. A series with unit root is said to be un-stationary and does not follow

random walk. There are three most popular dickey-fuller tests for testing unit root

in a series.

The above equation can be rewritten as:

∆ r t = δ r t-1 + u t

Here δ = (ρ-1) and here it is tested if δ is equal to zero. r t is random walk if δ is

equal to zero. It is possible that time series could behave as a random walk with

a drift. This means that the value of r t may not center to zero and thus a constant

should be added to the random walk equation. A linear trend value could also be

added align with the constant it the equation, which results in a null hypothesis

reflecting stationary deviations from trend.

The Augmented Dickey-fuller Test:




In conducting the DF test as above, it is assumed that the error term u t was

uncorrelated. But in case the ut are correlated, Dickey and Fuller have developed

a test, known as the augmented Dickey- Fuller ( ADF) test. The ADF test

consists of estimating the following regression:

ΔY t = β1 + β2 t + δ Y t-1 + α i ΔY t-i + ε t

Where, εt is a pure white noise term and ΔYt-1 = (Yt-1-Yt-2), ΔYt-2 = (Yt-2-Yt-3),etc.

The number of lagged difference terms to include is often determined empirically,

the idea being to include enough terms so the error term in above equation is

serially correlated. In ADF we still test whether δ=0 and the ADF test follow the

same asymptotic distribution as the DF statistic, so the same critical value can be

used.

Limitation of Research

• The study conducted on the sample of six years starting from 2000 to

2006.

• The volatility in the market during two years was very high.

• S&P CNX 500 index used as a portfolio.




CHAPTER 4

DATA ANALYSIS




Analysis and Interpretation

Steps followed in the analysis-

• The data is collected for-

iv) NIFTY Index

v) NIFTY Futures

vi) S&P CNX 500.

• Period of data collection is 1st July,2000 to 31st march,2007

• The data is converted into log naturals to normalized the data to find out

any spurious correlations within the data sets.

• Then the data is tested for its stationarity using Augmented Dickey fuller

test

3.3 SAMPLE SIZE AND DATA SOURCES

In this study S&P CNX 500 has been considered as a proxy for the portfolio and

accordingly the closing index values were collected from July 1, 2000 till March 31,

2007. The daily observations were converted into continuous compounded returns in the

standard method as the log differences:

Rt = ln (It / It-1)

Where, It stands for the closing index value on day‘t’; The data is converted into lognaturals format to normalized the data to way out any spurious correlations within

the data sets.




ADF RESULT

NIFTY FUTURES

ADF Test

Statistic -17.2837 1% Critical Value* -3.4371

5% Critical Value -2.8637


NIFTY INDEX

ADF Test




S&P CNX 500

ADF Test







Interpretation

As it can be easily seen from the ADF test, the null hypothesis of unit root can be

rejected as the estimated τ value is 17.2837 for NIFTY Futures, 16.9875 for

NIFTY Index and 16.6139 for S&P CNX 500 Index , which in absolute value is

greater than all the critical value at 1%, 5% and 10% level of significance.

The absence of unit root means the series is stationary, combined with the

phenomenon of volatility clustering implies that volatility can be predicted and the

forecasting ability of the different models can be generalized to other time

periods also.




Residual stationary test

stationery test of rsiduals of fut n nifty

ADF Test Statistic -25.17931% Critical

Value* -3.4371

5% Critical Value -2.863710% Critical Value -2.5679

*MacKinnon critical values for rejection of hypothesis of a unit root.

Augmented Dickey-Fuller Test Equation

Dependent Variable: D(SER12)

Method: Least Squares

Date: 05/05/07 Time: 12:37

Sample(adjusted): 8 1731

Included observations: 1724 after adjusting endpoints

Variable CoefficientStd.Error t-Statistic Prob.

SER12(-1) -1.93776 0.076958 -25.1793 0

D(SER12(-1)) 0.583542 0.066863 8.727393 0

D(SER12(-2)) 0.368815 0.054351 6.785774 0

D(SER12(-3)) 0.217908 0.040113 5.43238 0

D(SER12(-4)) 0.099741 0.023948 4.164858 0

C 7.59E-06 8.23E-05 0.092229 0.9265

R-squared 0.657488Mean dependent

var 1.15E-06Adjusted R-squared 0.656491

S.D. dependentvar 0.005829

S.E. of regression 0.003417Akaike info

criterion -8.51691Sum squaredresid 0.020054 Schwarz criterion -8.49793

Log likelihood 7347.573 F-statistic 659.5771Durbin-Watsonstat 2.009048 Prob(F-statistic) 0




Nifty & S&P Residual test

stat test of res of nifty n snpADF TestStatistic -20.1187

1% CriticalValue* -3.4371

5% Critical Value -2.863710% Critical Value -2.5679





Date: 05/13/07 Time: 11:54




SER32(-1) -1.12818 0.056076 -20.1187 0

D(SER32(-1)) 0.2548 0.049484 5.149143 0

D(SER32(-2)) 0.129413 0.039857 3.246955 0.0012

D(SER32(-3)) -0.11591 0.031916 -3.63169 0.0003

D(SER32(-4)) 0.026371 0.024148 1.092064 0.275

C -2.39E-05 0.000305 -0.07848 0.9375

R-squared 0.498802

Mean dependent

var 2.58E-06Adjusted R-squared 0.49734


S.E. of regression 0.012644

Akaike infocriterion -5.89984

Sum squaredresid 0.274163 Schwarz criterion -5.88084





Nifty futures & S&P CNX 500

ADF TestStatistic -16.6139

1% CriticalValue* -3.4371







Date: 05/10/07 Time: 12:38




SER30(-1) -8.17E-01 0.049153 -16.6139 0

D(SER30(-1)) -0.04601 0.044993 -1.02269 0.3066

D(SER30(-2)) -0.13952 0.039027 -3.57498 4.00E-04

D(SER30(-3)) -0.11571 0.031713 -3.64846 0.0003

D(SER30(-4)) -0.02498 0.024121 -1.03539 0.3006

C 0.000537 0.000359 1.496878 0.1346

R-squared 0.447809

Mean dependent

var

-7.29E-

07Adjusted R-squared 0.446199


S.E. of regression 0.014825

Akaike infocriterion -5.58158

Sum squaredresid 0.376903 Schwarz criterion -5.56258





Interpretation

As it can be easily seen from the ADF test, the null hypothesis of unit root can be

rejected as the estimated τ value is 25.1793 for NIFTY Futures Vs Nifty , 20.1187

for NIFTY Index Vs S&P CNX 500 and 16.6139 for Nifty Futures Vs S&P CNX

500 Index , which in absolute value is greater than all the critical value at 1%, 5%

and 10% level of significance.

It also proves that there is correlation between Nifty Futures and Nifty, Nifty

Futures and S&P CNX 500 and Nifty Futures and S&P CNX 500




After finding Correlation Hedge Ration of Portfolio is found which is shown in the

table below:

Coefficients(a)Model

UnstandardizedCoefficients

StandardizedCoefficients T Sig.

B Std. Error Beta

1 (Constant) 216.077 4.93536943.7813

33.3E-

282

Snp 1.092546 0.002877 0.994073379.773

3 0

a Dependent Variable: futures

Here the ratio is 1.092546. Since the ratio is greater than 1 perfect hedge ispossible.




CHAPTER 5

CONCLUSION




CONCLUSION

After that theoretical future price was calculated using S(1+Rn) Where s is the

spot price, r is the risk free rate(t-bills rate), n is no of days Then the theoretical

price is compared with actual and the difference is known as basis.

We took the T Bills annulized rate and coverted into monthly risk free return and

use in finding out the theoretical price of NIFTY futures. Then we calculated the

difference between the actual futures price & theoretical futures price, Which is

known as basis.

We took the monthly average of basis (actual price – theoretical price) and apply

“t” test which shows that the basis risk is exist or not.

After applying “t” test for the above mentioned data we found that basis risk

exist in the market.

.




BIBLIOGRAPHY

BOOKS

1. Basic Econometrics: By Damodar N. Gujrati

2. Introductory Econometrics: By Ramu Ramanathan

WEBSITES

1. www.nseindia.com

2. www.yahoofinance.com

ECONOMETRICS SOFTWARE PACKAGES

1. Eviews

2. SPSS

References

1. Ronald W. Anderson; Jean-Pierre Danthine “Cross Hedging”,

The Journal of Political Economy , Vol. 89, No. 6. (Dec., 1981), pp. 1182-1196.

2. Philip Garcia; Raymond M. Leuthold; Mohamed E. Sarhan



“Basis Risk: Measurement and Analysis of Basis Fluctuations for Selected

LivestockMarkets”,American Journal of Agricultural Economics, Vol. 66, No. 4.

(Nov., 1984), pp. 499-504.

3. Warren Bailey; K. C. Chan“ Macroeconomic Influences and the Variability

of the Commodity Futures Basis”,The Journal of Finance, Vol. 48, No. 2.

(Jun., 1993), pp. 555-573.

4. Bradford Cornell; Kenneth R. French“Taxes and the Pricing of Stock Index

Futures”,The Journal of Finance, Vol. 38, No. 3. (Jun., 1983), pp. 675-694.

5. James D. Sartwelle, III , Edward Smith, Terry Kastens and Daniel

O’Brien,“Selling Hedge with Futures”, The Texas A&M University system

6. James D. Sartwelle, III , Edward Smith, Terry Kastens and Daniel

O’Brien,“Buying Hedge with Futures”, The Texas A&M University

system

Kavita Bhansali-05-Hedging performance

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